论文标题
黑洞散射和分区功能
Black Hole Scattering and Partition Functions
论文作者
论文摘要
当计算黑洞范围外的标量的理想气体热典型分区函数时，由于正常模式频谱的连续性，人们会遇到状态的不同单粒子密度（DOS）。将Lorentzian场方程重新铸造为有效的一维散射问题，我们认为散射阶段编码有关DOS的非平凡信息，并且可以通过“重新归一化” DOS来提取有关参考的DOS。这将重新归一化的自由能定义为任意添加剂常数。有趣的是，由DENEF-HARTNOLL-SACHDEV公式计算得出的1循环欧几里得路径积分将参考自由能固定为在Rindler空间上，而重新归一化的DOS捕获了标量的准模式。我们以静态BTZ，Nariai黑洞和DE Sitter静态贴片的标量为例来支持这些主张。对于渐近平坦空间中的黑洞，重新归一化的DOS是由透射系数的相位捕获的，其幅度平方是灰体因子。我们从代数的角度对最近的作品进行了评论。
When computing the ideal gas thermal canonical partition function for a scalar outside a black hole horizon, one encounters the divergent single-particle density of states (DOS) due to the continuous nature of the normal mode spectrum. Recasting the Lorentzian field equation into an effective 1D scattering problem, we argue that the scattering phases encode non-trivial information about the DOS and can be extracted by "renormalizing" the DOS with respect to a reference. This defines a renormalized free energy up to an arbitrary additive constant. Interestingly, the 1-loop Euclidean path integral, as computed by the Denef-Hartnoll-Sachdev formula, fixes the reference free energy to be that on a Rindler space, and the renormalized DOS captures the quasinormal modes for the scalar. We support these claims with the examples of scalars on static BTZ, Nariai black holes and the de Sitter static patch. For black holes in asymptotically flat space, the renormalized DOS is captured by the phase of the transmission coefficient whose magnitude squared is the greybody factor. We comment on possible connections with recent works from an algebraic point of view.
